Sound Absorption Coefficient of Glass Wool

By Sadao Aso and Rikuhiro Kinoshita, Members, TMSJ

Faculty of Engineering, Tokyo University of Agriculture

and Technology, Koganei, Tokyo.

Based on the Journal of the Textile Machinery Society of Japan, Transactions, Vol, 18, No. 11, T 649-653 (1965)

Abstract This article presents the results of an investigation into the relation between the normal incident sound absorption coefficient and the apparent density of glass wool boards used as a sound absorbent.

(1) Only one kind of glass wool boards 64 kg/m3 in apparent density and 2.5 cm in thickness out of 20 kinds made by 3 manufacturers has given a sound absorption characteristic belonging to the mixed type. The sound absorption characteristics of the other kinds of glass wool boards have been shown by experiment to belong to the viscosity-resistance type.

(2) The relation between effective apparent density Dea (kg/m3) at which a glass wool board gives 1.00 in sound absorption coefficient and the thickness T (cm) is :

Dea=aT -b where a and b are constants fixed by the manufacturer.

(3) The relation among apparent density Da (kg/m3), thickness T (cm), distance d (cm) between the center of a sample and the rigid wall, and frequency f o at which the sample gives the maximum sound absorption coefficient is expressed by the follow-ing empirical formula :

f0= (c/4-aD3a'T)d-' where a and t are constants and c is the speed of sound.

1. Introduction

Previous articles reported on the influence which several factors in the make-up of a fiber assembly

have on sound absorption characteristics[1] ; the rela-tionship between the maximum absorption coefficient

and those factors; and the effective porosity of sound-

absorbing fibrous materials[2]. The present article deals with the relation between the sound absorption

characteristics and the apparent density of commercially

sold glass wool boards which are representative of many kinds of sound-absorbing fibrous materials.

2. Method of Experimenting

There are the reverberation room method and the

tube method to measure the sound absorption coef f i-

cient of materials. We measured the normal incident

sound absorption coefficient (abbreviated here to "sound absorption coefficient") by the tube method . The theory and apparatus for measuring sound absorp-tion coefficient are the same as those we used to measure the sound absorption coefficient of f abrics[3]. Sound absorption coefficients were measured from 250 c/s to 2000 c/s at intervals of 1/3 octaves generally. Where necessary, we also made measurements with frequencies in between.

We used, as samples, 20 kinds of glass wool boards, 61 cm by 91.5 cm in size, made by three manufacturers in Japan. Their nominal thickness and apparent density are given in Table 1. Many specimens, 10cm in diameter, were cut out of the glass wool boards, with a circular punch installed in a drill press. The apparent density of the specimens fluctuated, making an observed apparent density generally different from the nominal apparent density of the glass wool board.

Five or six specimens were picked out of many belonging to one kind of glass wool board in such a

Vol. 12, No. 3 (1966) 101

way they would differ in apparent density from one another at about regular intervals. Each specimen

picked out was inlaid into a ring having the same thickness as the specimen, and was then put in a measuring tube in such a way that it had an air space behind it. The idea of the air space behind the specimens was to obtain, within the limits of measured frequencies, the maximum sound absorption coefficient of a specimen small in apparent density or of a specimen small in thickness.

3. Types of Absorption Characteristics

A previous article[2] classified the types of absorp-tion characteristics of fiber assemblies into 4 : the viscosity resistance type, the mixed type, the fibrous resonance type and the board resonance type. The article made it clear that the absorption characteristics of fiber assemblies changed from the viscosity resis-tance type to, successively, the mixed type and the resonance type as they decreased in porosity. Fig. 1 shows the absorption characteristics of glass

wool boards differing in apparent density (Da), namely,

porosity (P) . Porosity was calculated with the specific gravity of a glass fiber as 2.49. Samples Nos. 7 and 8 belong to the viscosity resistance type.

Although sample No. 11 should have been classified as of the mixed type in its absorption characteristics, we treated it as of the viscosity resistance type, be-cause sound absorption belonging to the viscosity resistance type was predominant in its characteristic and because the maximum absorption coefficient at about 900 c/s acquires the properties of sound absorp-tion attributed to the mechanism of the viscosity resistance type. Sample No. 12 is a typical mixed type. The larger

a sample is in thickness, the more readily its absorption characteristic changes from the viscosity resistance type to the mixed type at a high porosity degree. However, sample No. 12 excepted, we were able to treat all samples, even those 5 cm thick, as of the viscosity resistance type.

4. Maximum Absorption Coefficient and

Apparent Density

The absorption characteristics of the specimens of all kinds of glass wool boards were obtained by keeping

Table 1 Dimension of Glass

and Manufacturers

Wool Boards Measured

Fig. 1 Sound absorption characteristics of

boards 2.5 cm thick

Da : Observed apparent density

P : Porosity

glass wool

102 Journal of The Textile Machinery Society of Japan

the distance between the front surface of a specimen

and the rigid wall in the measuring tube at 8.5 cm.

Accordingly, the air space behind a specimen differed

in depth as the glass wool boards differed in thickness.

One example is Fig. 2 which gives the absorption

characteristics of 5 specimens belonging to No. 11 and

the characteristics of the remainder were shown in

Fig. 1. The figures illustrate that sound absorption

coefficient increases as apparent density increases ;

and that the maximum absorption coefficient is influ-

enced extremely by apparent density. The order of

apparent density in No. 11 coincided with the maximum

absorption coefficient, but this was not the case with

every sample. Even a specimen having a large value

in apparent density is small in sound absorption coeffi-

cient if it has a big space in it or if its air channel

runs straight from the front surface to the back

surface of the specimen.

Fig. 3 shows the relationship between the maximum

absorption coefficient and apparent density for 9 kinds

of glass wool boards manufactured by A & Co. If

they are uniform in thickness, their maximum absorp-

tion coefficient increases with an increase in their

apparent density and reaches 1.00 at a certain value

of apparent density. We call this apparent density

"effective apparent density Pea of the glass wool

board." The values of Dea for the glass wool boards

made by the 3 manufacturing firms are given in Table

2. The values for the glass wool boards manufactured

by C & Co. are the smallest of all. This shows

clearly that C & Co. 's products are made of the finest

of glass fibers used by the 3 firms.

Fig. 2 Sound absorption characteristics of

belonging to sample No. 10

Da : observed apparent density

specimens

Table 2 Effective Apparent Density Dea (kg/m3)

Table 3 Constants a and b in Empirical Formula Dea=aT _6

Dea : Effective apparent density (kg/m3) T : Thickness (cm)

Fig. 3 Bearing of thickness on relation between maximum absorption coefficient and observed

apparent density of glass wool boards manu-

factured by A & Co.

Vol. 12, No. 3 (1966) 103

The relation between Dea and thickness T of samples made by A & Co. is, as shown in Fig. 4, a line on log-log section paper. Accordingly, this relation is given by the following formula :

Dea=aT-b .........(1) where a and b are constants.

A fiber assembly has an effective porosity Fe (9o), at which the maximum absorption coefficient reaches 1.00, and the relation between Fe and T is :

(100-Fe) =a'T -b' where a' and b' are constants.C2]

It seems, therefore, that eq. (1) holds good for the glass wool boards made by B & Co. and C & Co., although measured samples were only 2.5 or 5.0 cm thick. Constants a and b in eq. (1) calculated from meas-ured results are given in Table 3. The Dea for a

glass wool board having an optional thickness is calcul-able from eq. (1). Each manufacturer sells glass wool boards of the same nominal apparent density but of different thicknesses. However, they can be reduced in apparent density by increasing their thickness.

5. Frequency

Coefficient

at Which the Absorption

is the Maximum

We measured the sound absorption coefficients of a fiber assembly belonging to the viscosity resistance type by assuming an air space behind it. In this case, the relation between frequency f o (c/s), at which the absorption coefficient in the absorption characte-ristic reached a maximum, and the distance d (cm)

between the rigid wall and the center of the sample was.: [2]

f o=Kd-1 .........(2) where K was a constant decided by the sample. Eq. (2) can be used fully if the relation between K and a factor in the make-up of a glass wool board is established. With this in mind, we chose 9 spe-cimens having an observed apparent density closest to the nominal apparent density, from among many spe-cimens cut off from glass wool boards of various thicknesses made by A & Co. Table 4 shows their observed apparent densities. The absorption charac-teristics of the specimens were obtained by varying distance L between the front surface of a specimen and the rigid wall from 2.5 cm to 5.0 and 15.0 cm.

Fig. 4 Relation between

Dea and thickness

manufactured by

effective apparent

of the glass wool

A & Co.

density

boardsTable 4 Observed Apparent Density Da (kg/m3) of

Specimens Whose Sound Absorption Charac-teristics Were Obtained by Varying Depth of Air Space

Fig. 5 Bearing which depth of air space has on sound absorption characteristics of specimen 11.8 kg/m3 in observed apparent density (L is distance

between front surface of specimen and rigid wall)

104 Journal o f The Textile Machinery Society o f Japan

One example is Fig. 5, giving the absorption characteristics of a specimen 2.5 cm in thickness and 11.8 kg/m in apparent density. The maximum absorp-tion coefficients in absorption characteristic at each L were almost fixed. Accordingly, although we have discussed effective apparent density Dea under the condition L=8.5 cm, we may conclude that the value of Dea is unchanged, irrespective of the depth of the air space. By substituting the observed f n and d into eq. (2), we obtained K of the values given in Table 5. K for each sample is regarded as a constant. In other words, eq. (2) holds good for each sample. As for the specimen T =5.O cm and De=24.3 kg/m, it was difficult to f o because the curve in the neighborhood of the maximum absorption coefficient in the absorption characteristic was flat.

If a standing wave which is f o (c/s) in is in a measuring tube empty of samples,

particle velocity of air is the maximum at cm from the rigid wall, then the relation and d is :

f o = c/4 d -1 (c: sound speed in air

frequency

and if the

distallce d between f o

cm/sec)

If a sample belonging to the viscosity resistance type is placed at a place where particle velocity is the maxi-mum, the absorption coefficient is the maximum. However, since the sound speed in the sample belonging to the viscosity type slows down, K<c/4. If a sample decreases in thickness to an infinitesimal, K=c/4= 8600. The relation between the mean value of K for each sample and thickness T is as shown in Fig. 6 and expressible by the following formula :

K=c/4-kT .........(3)

Table 5 Values of K Obtained by Substituting into eq. (2) Frequency f o at Which a Specimen Gives the Maxi-mum Sound Absorption Coefficient in an Absorption Characteristic and Distance d between the Center of the Specimen and Rigid Wall

Fig. 6 Relation

by A&

between thickness

Co. and constant K

T of samples made in eq. (2)

Fig. 7 Relation between observed Da of samples made by A

stant k in eq. (3)

apparent density

& Co. and con-

Vol. 12, No. 3 (1966) 105

where K is a constant decided by apparent density. Since the observed apparent density Da of speci-

mens belonging to a certain nominal apparent density fluctuates as in Table 4, the values of K in Fig. 6 deviate up and down from the lines of eq. (3), depend-ing on the values of Da. The relation between k computed by the method of least squares and the mean value of Da by which k is obtained makes a line on log-log section paper

(see Fig. 7). Accordingly : k=aDas .........(4)

where x and Q are constants and where, for glass wool boards manufactured by A & Co., a=100 and j9 =0.606. Substituting eqs. (3) and (4) into eq. (2)

yields the following empirical formula : fo=(c/4-aDas,T)d-' .........(5)

If d is so fixed as to make eq. (5) valid, a glass wool board absorbs a sound of certain frequency f U most. If a sample having an effective apparent density gives 1.00 in sound absorption coefficient at the frequency

just mentioned.

6. Conclusions

In the light of the results of studies on the sound absorption characteristics of a fiber assembly, we have discussed the relation between sound absorption coe-fficient and apparent density of commercially sold

glass wool boards. The results given in this article should be of interest to those making practical use of

glass wool boards. It is to be hoped that a glass wool board having an apparent density which corresponds to effective apparent density will come on the market.

Absorption coefficients in our experiment were measured at Kobayashi Institute of Physical Research. The authors are deeply grateful to Mr. Masaru Koyasu of the institute for his suggestions, advice and supply of glass wool boards for the experiment.

Reference

[1] S. Aso and R. Kinoshita : J. Text. Mach. Soc. Japan ; English edition, Vol. 10, No. 5, 209(1964)

[2] S. Aso and R. Kinoshita : J. Text. Mach. Soc. Japan: English edition, Vol. 11, No. 3, 81(1965)

[3] S. Aso and R. Kinoshita : J. Text Mach. Soc. Japan; English edition, Vol. 9 No. 1, 1(1963)

106 Journal of The Textile Machinery Society of Japan